Via an exploit no, there is a thing called cogswap but to my knowledge it does not work 100% (yet) also i don't think you can use a exploit on a slim Ps2 like you can in the bulky Ps2 as Sony fixed the code for on the Slim Ps2.
About Cogswap, if I put it on my memory card, does that mean my backups will automatically load when I put them in or will there be a procedure I'll have to go through to load them? And does it work with the slim ps2s? It seems like you said it didn't.
I found this guide ( http://www.exploitstation.com/articles/cogswap%20guide.php ) to installing the exploit (seems better than the ps1 game method), but I was wondering what kind of cheat device I would need. I'd like to get the cheapest one possible, so that would be an older version, and I wanted to know if older versions didn't work.
Action Replay MAX (EVO) v3.30 (not 3.34 like they're selling now) supports loading any elf file from a thumb drive, and I worked for me until the disc got too scratched. I bought a new one (3.34) and the only elf files working now are the HDLoader/USBAdvance series and the emulators. No loaders work to my avail.
With ARMAX v3.30 load COGSWAP.ELF to a thumb drive and run it with the max media player. If you don't know what to do from there I don't want to help you.